SOLUTION: Find the area of the polygon whose vertices are at (1,-4),(4,-1),(4,5),(-1,4)&(-2,-1).

Algebra ->  Length-and-distance -> SOLUTION: Find the area of the polygon whose vertices are at (1,-4),(4,-1),(4,5),(-1,4)&(-2,-1).      Log On


   

Question 166152: Find the area of the polygon whose vertices are at (1,-4),(4,-1),(4,5),(-1,4)&(-2,-1).
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
First plot the points and see what you've got.

Define a couple of extra points that will help simplify the solution.
X at (4,4)
Y at (-1,-1)

Now we can find the areas of the individual triangles and square and add them together.
Area of a square is s*s where s is the side length.
Area of a triagle is half the product of base and height.
.
.
.
Square BXDY : A=s%5E2=5%5E2=25
Triangle XCD :A=%281%2F2%29bh=%281%2F2%29%285%29%281%29=5%2F2
Triangle DEY :A=%281%2F2%29bh=%281%2F2%29%281%29%285%29=5%2F2
Triangle EAB :A=%281%2F2%29bh=%281%2F2%29%286%29%283%29=9
Now add all of the areas,
A%5Bp%5D=25%2B5%2F2%2B5%2F2%2B9
A%5Bp%5D=39